The Science of the Shulba: A Study in Early Hindu Geometry c10.76

c10.76

The methods suggested by Āpastamba for the same purpose will be understood from those adopted by him for the construction of the *Mahāvedi*. The shape of the *Mahāvedi* is prescribed by tradition to be an isosceles trapezium whose altitude is 36 *pada* (or *prakrama*), face 24 (units) and base 30 (units). Āpastamba gives four methods for its construction. All of them are in principle the same. It is to draw a straight line through both the extremities of another straight line equal to the given altitude and at right angles to it. Along these straight lines and on other sides of the altitude are measured lengths equal to half the given lengths of the face and the base. And thus the isosceles trapezium is drawn. Āpastamba distinguishes between his different methods as *Ekarajjvāviharaṇa* ("The method of construction with one cord") and *Dvirajjvāviharaṇa* ("The method of construction with two cords").